Strain localisation patterns under equal-channel angular pressing

Instabilities of plastic flow in the form of localised shear bands were experimentally observed to result from equal-channel angular pressing (ECAP) of magnesium alloy AZ31. The appearance of shear bands and their spacing were dependent on velocity of the pressing and applied back-pressure. A generic gradient plasticity theory involving second-order strain gradient terms in a constitutive model was applied to the case of AZ31 deformed by ECAP. Linear stability analysis was applied to the set of equations describing the deformation behaviour in the process zone idealised as a planar shear zone. A full analytical solution providing a dispersion relation between the rate of growth of a perturbation and the wave number was obtained. It was shown that the pattern of incipient localised shear bands exhibits a spectrum of characteristic lengths corresponding to admissible wave numbers. The interval of the spectrum of wave numbers of viable, i.e. growing, perturbations predicted by linear stability analysis was shown to be in good agreement with the experimentally observed spectrum. The effect of back-pressure applied during ECAP was also considered. The predicted displacement of the shear band spectrum towards lower wave numbers, shown to be a result of the decreased shear strain rate in the shear zone, was consistent with the experimentally observed increase of the band spacing with increased back-pressure. A good predictive capability of the general modelling frame used in conjunction with linear stability analysis was thus demonstrated in the instance of the particular alloy system and the specific processing conditions considered.